In the framework of the theory of open systems based on completely positivequantum dynamical semigroups, we give a description of the continuous-variablequantum entanglement and quantum discord for a system consisting of twononinteracting modes embedded in a thermal environment. Entanglement anddiscord are used to quantify the quantum correlations of the system. For allvalues of the temperature of the thermal reservoir, an initial separableGaussian state remains separable for all times. We study the time evolution oflogarithmic negativity, which characterizes the degree of entanglement, andshow that in the case of an entangled initial Gaussian state, entanglementsuppression (entanglement sudden death) takes place, for non-zero temperaturesof the environment. Only for a zero temperature of the thermal bath the initialentangled state remains entangled for finite times. We analyze the timeevolution of the Gaussian quantum discord, which is a measure of all quantumcorrelations in the bipartite state, including entanglement, and show thatquantum discord decays asymptotically in time under the effect of the thermalbath. This is contrast with the sudden death of entanglement. Before thesuppression of the entanglement, the qualitative evolution of quantum discordis very similar to that of the entanglement. We describe also the timeevolution of the degree of classical correlations and of quantum mutualinformation, which measures the total correlations of the quantum system.
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